Solve the following: 2x + y = 15 y = 4x + 3​

The Pigeon-hole Principle states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon. This proves that among any group of d+1 integers there are two with exactly the same remainder when divided by d.

This concept can be applied to your question: If there are d+1 integers, and we divide each of them by d, there are at most d remainders that can be obtained. This means that two of the integers must have the same remainder when divided by d.
To prove this, let us assume that all d+1 integers have different remainders when divided by d. Then the remainders must range from 0 to d-1. For example, if d=5, then the remainders must be 0, 1, 2, 3 and 4. Let us denote the integers by x0, x1, x2, ... , xd. Now we can apply the Pigeon-hole Principle. We have d+1 pigeons (x0, x1, x2, ... , xd) and d pigeonholes (remainders 0, 1, 2, 3, 4). Since d+1 is greater than d, at least one pigeonhole must contain more than one pigeon. This means that two of the integers must have the same remainder when divided by d.

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The insufficient evidence to suggest that a higher proportion of Seniors are attending Prom than Juniors.

1. STATE:Parameter: proportion of Juniors attending Prom, proportion of Seniors attending PromStatistic: the sample proportions of Juniors and Seniors who are planning on attending PromHypotheses:H0: pJ = pS (the proportion of Juniors attending Prom is equal to the proportion of Seniors attending Prom)Ha: pJ < pS (the proportion of Juniors attending Prom is less than the proportion of Seniors attending Prom)Significance level: α = 0.05 (5%)2. PLAN:Procedure: two-sample z-test for proportionsConditions:Randomization: The students were randomly selected from each grade level.Independence: The samples are independent as they come from different grade levels.Large Sample: npJ ≥ 10, n(1 − pJ) ≥ 10, npS ≥ 10, n(1 − pS) ≥ 103. DO:Mean:pJ − pSPicture:Standard deviation:Formula:General formula: Z = (pJ − pS) / SEpJ = number of Juniors who are planning to attend Prom / sample size of JuniorsnJ = sample size of JuniorspS = number of Seniors who are planning to attend Prom / sample size of SeniorsnS = sample size of SeniorsSE = sqrt[(pJ(1 - pJ))/nJ + (pS(1 - pS))/nS]Specific formula: Z = (0.56 - 0.64) / 0.092 = -0.87Test statistic: Z = -0.87P-value:P(Z < -0.87) = 0.1935Because the p-value (0.1935) is greater than the significance level (0.05), we fail to reject the null hypothesis. There is insufficient evidence to suggest that a higher proportion of Seniors are attending Prom than Juniors.

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Answer:

D. 24 ft

Step-by-step explanation:

Congruent means equal. Since ABCD and PQRS are congruent they are the same.

Answer:

D

Step-by-step explanation:

The tangential component of the acceleration vector at point t = 1 is aT(1) = 233/3 and The normal component of the acceleration vector at point t = 1 is aN(1) = (1/3)√10459

The acceleration vector can be found from the following formula:

[tex]a(t) = r''(t) = (-3,-10t,-8t3).[/tex]

To find the tangential component of the acceleration vector, we first need the velocity vector v(t).

[tex]v(t) = r'(t) = (-3,-10t,-8t3) .[/tex]

Next, we need to normalize the velocity vector using the following formula:

[tex]T(t) = v(t) / ||v(t)||,[/tex]

Where ||v(t)|| is the magnitude of the velocity vector.

[tex](1) = (-3,-10,-8) / \sqrt{(3^2 + 10^2 + 8^2)} = (-3/3, -10/3, -8/3) = (-1 , -10/3, -8/3) .[/tex]

Then, the tangential component of a(1) is:

[tex]aT(1) = a(1) T(1) = (-3, -10, -8) (-1, -10/3, -8/3) = 3 + 100/3 + 64/3 = 233/3.[/tex]

To find the normal component of a(1), we simply need to find the magnitude of the tangential component and subtract it from the magnitude of the acceleration vector.

[tex]aN(1) = \sqrt{ (a^2 - aT(1)^2)} = \sqrt{(3^2 + (10)^2 + (8)^2 - (233/3)^ 2)}  = \sqrt{(9 + 100 + 64 - 54289/9)} = \sqrt{(10459/9)} = (1/3)\sqrt{10459}[/tex]

Therefore, the tangential and normal components of the acceleration vector at the point t = 1 are:

[tex]aT(1) = 233/3[/tex] and [tex]aN(1) = (1/3)\sqrt{10459}[/tex]

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The probability that at most of the parts are defective is 0.96.

A machine that manufactures automobile parts produces defective parts of the time. If parts produced by this machine are randomly selected, what is the probability that at most of the parts are defective?

The given probability of producing defective parts is P(defective) = 0.15. Now, we need to find the probability that at most of the parts are defective. This can be done by finding the probability of producing 0, 1, or 2 defective parts.

Let X denotes the number of defective parts. So, we have to calculate the probabilities for P(X = 0), P(X = 1), and P(X = 2). To calculate these probabilities, we will use the binomial probability formula:

P(X = x) ={n}C{x} p^x (1 - p)^{n - x}, Here, n = number of parts produced, p = probability of producing defective parts

x = number of defective parts

First, we need to find P(X = 0),

P(X = 0) = (0.85)^5 = 0.4437

P(X = 1) = {5}C{1} (0.15)^1 (0.85)^4 = 0.3672

P(X = 2) = {5}C{2} (0.15)^2 (0.85)^3 = 0.1459

Now, we can find the probability that at most of the parts are defective as follows:

P{at most 2 defective parts}) = P(X = 0) + P(X = 1) + P(X = 2) = 0.957

Therefore, the probability that at most of the parts are defective is 0.96.

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Wilson and William were measured at various times, therefore drawing the inference that Wilson grew more over the course of a year than William is incorrect and the statistics is misleading.

Inferential statistics and descriptive statistics are two disciplines of statistics with distinct applications.

Summarizing and characterizing gathered data is the focus of descriptive statistics. It uses techniques including graphical presentations, measurements of variability, and measures of central tendency, such as mean, median, and mode (e.g., histograms, box plots). The purpose of descriptive statistics is to shed light on a sample's or population's properties, such as its distribution, dispersion, and shape.

Wilson and William were measured at various times, therefore drawing the inference that Wilson grew more over the course of a year than William is incorrect.

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Answer:

Zeros: x = -10 and x = -3

Vertex: [tex](-\frac{13}{2} , \frac{49}{4} )[/tex]

Step-by-step explanation:

We are given the following function:
f(x) = -(x+3)(x+10)

We want to find the zeros and the vertex of the parabola.

The zeros are the values of the function where f(x) = 0.

So, in order to find the zeros, we can set f(x) = 0.

0 = -(x+3)(x+10)

We can divide both sides by -1, to get:

0 = (x+3)(x+10)

To solve this, we will use zero product property.
Split and solve:

x+3 = 0

x = -3

x+10=0

x = -10

Now, to find the vertex, we first get the average of the zeros.

Add the values of the zeros together, then divide by two:

[tex]\frac{-3-10}{2}[/tex] = [tex]\frac{-13}{2}[/tex]

Now, we plug this in for x to get the y value (found through f(x)) of the vertex.

[tex]f(-\frac{13}{2}) = -(-\frac{13}{2} + 3) (-\frac{13}{2} + 10)[/tex] = [tex]\frac{49}{9}[/tex]

So, the vertex is [tex](-\frac{13}{2} , \frac{49}{4} )[/tex]

The interest which josh will pay on the electric scooter with a simple annual interest of 3% is 7.50.

Interest rate can be defined as the amount of interest which is due per period, as a proportion of the amount lent, deposited, or borrowed by someone.

The interest rate formula is:

Interest Rate = {(Simple Interest × 100)}/{ (Principal × Time)}

Here,

Josh borrowed 250 from his mother to buy an electric scooter and will pay her back in one year with three simple annual interest.

The amount of interest that Josh will pay is calculated as:

Interest = Principal Amount × Rate of Interest × Time

Interest = 250 × 3

Therefore, Josh will pay his mother $7.50 in interest for the loan.

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Answer:

p = 0, p = -7/3

Step-by-step explanation:

We are given the following equation:
3p² + 7p = 0

We want to solve the equation by factoring.

To factor, we want to look for a common term that we can pull out.

You may notice that both terms have 'p' in common, so we can pull out p from both terms.

This will then make the equation:

p(3p + 7) = 0

Now, we can use zero product property to solve the equation.

p = 0

3p + 7 = 0

Subtract.

3p = -7

Divide.

p = -7/3

Our answers are p = 0 and p = -7/3

Answer:

See below picture.

Explanation:

y=2 has a y-intercept of 2, so we start graphing there. with most equations, we would follow the slope starting from that point, but y=2 doesn't have a slope. The 2 stays going all the way "across" for all x-values. I used demos to graph.

Answer:

Step-by-step explanation:

(3x+1)^2 = 3x+3

9x^2 +6x +1=3x+3

9x^2+3x-2=0

finally we got a trinomial quadratic equation solve by factorizing

9x^2 -6x+3x-2=0

3x(3x-2)+(3x-2)=0

3x-2 = 0 or 3x+1=0

x= 2/3 or x= -1/3

Since both terms are perfect squares, factor using the difference of squares formula, [tex]a^2-b^2=(a+b)(a-b)[/tex] where [tex]a=b[/tex] and [tex]b=3[/tex]

Answer:

x = -4

y = -3

Step-by-step explanation:

-5y + 3x = 3

-8y + 9x = -12​

Time the first equation by -3

15y - 9x = -9

-8y + 9x = -12

7y = -21

y = -3

Now put -3 in for y and solve for x

-5(-3) + 3x = 3

15 + 3x = 3

3x = -12

x = -4

Let's Check

-5(-3) + 3(-4) = 3

15 - 12 = 3

3 = 3

So, x = -4 and y = -3 is the correct answer.

To construct a histogram of the estimates and compare it to the above estimates, follow these steps:
1. Compile the data and organize it into groups or bins.
2. Assign each group a height or frequency, usually the number of occurrences in the group.
3. Represent each group by drawing a bar with the corresponding height.
4. Connect the tops of the bars to form a histogram.

Comparing the histogram to the above estimates, if the histogram is similar in shape and spread, then the estimates are consistent.

The best estimate of the random modifier without examining the value is the mode of the data, which is the value that occurs most often.

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As per the combination method, the number of tickets that we put in that are marked "outer" is 3 (option d).

In this case, we want to choose the number of tickets marked "outer." Let's call this number k. We know that we already put one ticket marked "inner" in the box, so the total number of tickets in the box is 2. Therefore, n = 2.

Now we need to determine k. We want to know how many tickets we need to put in that are marked "outer." We can represent this as a. So we have:

ᵃC₁ = a! / ((1!)(a-1)!) = a

We want to find the value of a that satisfies the condition that the probability of choosing an "inner" ticket is 1/3 and the probability of choosing an "outer" ticket is 3/2.

Since we already put in 1 ticket marked "inner," the probability of choosing an "inner" ticket is 1/2, which means the probability of choosing an "outer" ticket is also 1/2.

We know that the probability of choosing an "outer" ticket is 3/2, so we can set up the following equation:

ᵃC₁ / 2 = 3/2

Solving for a, we get:

a = 3

In conclusion, the answer is (d) 3.

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Out of the given options, Jarrod can get the most accurate results by surveying the people wearing the home team's jersey. Therefore, the correct option is D.

A survey is an organized process of collecting and recording information from a particular group of people for the purpose of understanding and discovering the state of affairs in a particular area or issue. It is one of the most prevalent research methods used by social scientists and market researchers, among others. Surveys are used to obtain accurate data on a variety of topics, such as people's opinions and behaviors, demographic data, socioeconomic data, and much more.

Accurate surveying is critical because it assists in collecting precise data, which is critical in making sound decisions. An accurate survey provides the data needed to establish reliable conclusions, identify trends, and draw meaningful insights.

The method of conducting a survey can influence the outcome; therefore, it is critical to use the most effective approach to get accurate data.

To get the most accurate results from a survey, a researcher must be sure to construct the questionnaire correctly and analyze the data effectively.

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Answer:

TAN is a mathematical function in trigonometry that stands for tangent. It is used to calculate the tangent of an angle in a right triangle, which is defined as the ratio of the length of the opposite side to the length of the adjacent side.

In equations, you can use TAN to find the value of the tangent of an angle. For example, if you have an angle of 30 degrees in a right triangle and you want to find the value of the tangent of that angle, you can use the TAN function in your calculator or programming language.

The syntax of the TAN function is usually "tan(x)", where x is the angle in radians. If your calculator or programming language uses degrees instead of radians, you may need to convert the angle to radians first using the conversion formula: radians = degrees * (pi/180).

For example, to find the value of the tangent of 30 degrees, you can use the TAN function as follows:

In degrees mode: TAN(30) = 0.57735027

In radians mode: TAN(30*pi/180) = 0.57735027

TAN can be used in various trigonometric equations and identities to solve for unknown sides or angles of a right triangle.

Step-by-step explanation:

A circle is a shape formed by a point moving in a plane while keeping the same distance from a fixed point. The measurement of angle EDF is 23 degrees.

To start, a circle is a shape that is created by a point moving in a plane while its distance from a fixed point remains constant. This fixed point is called the center of the circle.

Since we know that angles created by the same chord in a circle are equal, we can use this information to find the measure of angle EDF.

In this case, EF is the chord of the circle, and we are given that angle EGF measures 23°. Therefore, we can conclude that angle EDF must also measure 23° since it is created by the same chord EF.

Thus, we can say that the size of angle EDF is 23°.

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Complete question is the image attached below

The condition that must be true in order for a confidence interval based on de Moivre's equation to be valid is:

d. The underlying distribution of the data must be normally distributed.

A confidence interval is an interval estimate of a population parameter that specifies a range of values within which the parameter is likely to lie with a certain level of confidence. In other words, it represents the degree of uncertainty associated with the estimate.

De Moivre's equation is a formula for approximating the probability of a specific number of successes in a series of independent Bernoulli trials. This formula is only relevant if the sample size is large enough such that the normal approximation to the binomial distribution is valid. Thus, this formula can be used to calculate confidence intervals for binomial proportions when the sample size is large enough to apply the normal approximation.

Answers to other options:

a. We must be forming a confidence interval for a coefficient in a multiple regression model - This statement is incorrect. De Moivre's equation is not related to multiple regression models.

b. All of these answers are correct - This statement is incorrect because not all of the options are correct. Only one option is correct.

c. We must be forming a confidence interval for a population mean based on a sample mean - This statement is incorrect. De Moivre's equation is not relevant for calculating confidence intervals for population means. The Central Limit Theorem is used instead.

Hence, option "d" only is true.

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Answer:

13) F(-5, 0), so F' will be at (1, 2)

G(-1, -1), so G' will be at (5, 1)

H(-2, 3), soH' will be at (4, 5)

14) G(-2, 1), so G' will be at (-1, 3)

H(-1, 3), so H' will be at (0, 5)

I(3, 1), so I' will be at (4, 3)

J(2, -1), so J' will be at (3, 1)

Step-by-step explanation:

13) Add 6 to each original x-coordinate and add 1 to each original y-coordinate.

14) Add 1 to each original x-coordinate and add 2 to each original y-coordinate.

You may plot the new points to confirm my answer.

We have that, if they put 40 chips in a hat, each one with the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10, and each number is put on four chips. Four tokens are drawn from the hat at random and without replacement, the value of q/p, q,p as probabilities, will be given by 360, therefore, the correct option is (D) 360

The probability that all four tokens have the same number (p) is equal to the total number of possible outcomes that meet that criterion divided by the total number of possible outcomes.

In this case, there are 10 possible numbers that could come up (1-10). Therefore, there are 10 possible outcomes for the four slips of paper that have the same number. Each outcome has the same probability of 1/10, so p = (1/10)^4 = 1/10000.

The probability that two of the slips have a number a and the other two have a number b (q) is equal to the total number of possible outcomes meeting that criterion divided by the total number of possible outcomes.

In this case, there are 10 possible numbers that could be drawn (1-10) and 2 ways to choose 2 different numbers out of 10, so there are 20 possible outcomes for two of the slips bearing a number and the other two bearing a number b. Each outcome has the same probability of 1/20, so q = (1/20)^4 = 1/3200000.

The ratio of q to p is q/p = 3200000/10000 = 360. Therefore, the value of q/p is 360.

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Andre can make 6 small cranes. X is the number of small cranes, 3x is the minutes, 10 is the minute for large cranes and 30 is the total time.

3x + 10 is less than or equal to 30

3 is the minutes for the small cranes

X is the number of small cranes

10 is the minutes for the large crane

30 is the total time limit

first, subtract 10 from 30, ( 30-10) which gives you 20 so

3x is less than or equal to 20.

To figure this out, divide 20 by 3, which gives you 6 as a quotient with a remainder of two minutes.

Andre can make 6 small cranes.

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The Complete question is

Andre is making paper cranes to decorate for a party. He plans to make one large paper crane for a centrepiece and several smaller paper cranes to put around the table. It takes Andre 10 minutes to make the centrepiece and 3 minutes to make each small crane. He will only have 30 minutes to make the paper cranes once he gets home.

​Andre wrote the inequality 3x + 10 ≤ 30 to plan his time. Describe what x, 3x, 10, and 30 represent in this inequality.

Solve Andre’s inequality and explain what the solution means.

Answer: The one that has the best deals.

Step-by-step explanation:

Angle L can be calculated as follows:

angle L = angle - 180 LMO stands for angle. MNO \sangle L = 180 - 150 - 30 degree angle L = 0

As a result, angle L is 0 degrees.

1. We know that sides AB and CD of trapezoid ABCD are parallel. We can use the tangent function to find the length of side AD because angle B is a right angle and angle ABD is 45 degrees:

AD/AB = tan(45)

AD=AB * tan(45) AD=AB

As a result, AD = 10.

2. We know that the sides PQ and RS of the trapezoid PQRS are parallel. We can use the sine function to find the length of side PS because angle Q is a right angle and angle PSQ is 60 degrees:

PS/QS sin(60) =

PS = sin * QS (60)

5 * sqrt = PS (3)

As a result, PS = 5*sqrt (3).

3. We know that the sides UV and WX of a trapezoid UVWX are parallel. We can use the cosine function to find the length of side WU because angle V is a right angle and angle WVU is 30 degrees:

WU/UV cos(30) =

UV * cos WU (30)

5 * sqrt(3) / 2 = WU

As a result, WU = (5/2)*sqrt (3).

4. We know that the sides LM and NO of the trapezoid LMNO are parallel. We can use the sine function to find the length of side MO because angle L is a right angle and angle MNO is 30 degrees:

MO/NO sin(30) =

MO = 4 / 2 MO = NO * sin(30)

As a result, MO = 2.

Because angles MNO and LMO add up to 180 degrees, we can calculate angle LMO as follows:

LMO angle = 180 - angle LMO MNO angle = 150 degrees

Finally, because angle N is a right angle, we can calculate angle L as follows:

angle L = angle - 180 LMO stands for angle. MNO\sangle L = 180 - 150 - 30 degree angle L = 0

As a result, angle L is 0 degrees.

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AAS conguerence rule states that if two congruent triangles have any two pairs of corresponding angles that are equal and one pair of corresponding sides that are equal.

Triangles that are congruent have the same area since all of their matching angles and side lengths are the same.

You are aware that a triangle's three angles add up to 180 degrees. As a result, the third pair of angles is also equal if the first two pairs are (180° - sum of equal angles). Hence, if any two pairs of angles and one pair of corresponding sides are equal, two triangles are said to be congruent. It could be referred to as the AAS Congruence Rule.

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The probability of getting the complete set of cards in Box 5 is 3/64.

To calculate the probability of getting the complete set of cards in Box 5, we have to consider the probability of getting each of the 4 cards in the previous 4 boxes.

For the first box,

The probability of getting any one of the 4 cards is 1,

since there are no previous boxes to consider.

For the second box,

The probability of getting a card that is not already in our possession is 3/4 (since there is one card already collected).

For the third box,

The probability of getting a card that is not already in our possession is 2/4 (since there are now two cards already collected).

For the fourth box,

The probability of getting a card that is not already in our possession is 1/4 (since there are now three cards already collected).

Multiplying these probabilities together, we get,

⇒ 1 x 3/4 x 2/4 x 1/4 = 3/64

So the probability of getting the complete set of cards in Box 5 is 3/64.

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Numerical integration involves approximating the definite integral of a function using numerical methods.

There are various techniques for numerical integration, including the Trapezoidal rule, Simpson's rule, and Gaussian quadrature.In general, these methods divide the integration interval into smaller sub-intervals and approximate the area under the curve within each sub-interval using mathematical formulas.

The approximations are then summed up to estimate the integral over the entire interval.The accuracy of the numerical integration depends on the number of sub-intervals used and the specific method used. Generally, increasing the number of sub-intervals leads to a more accurate approximation.

Overall, numerical integration is a useful tool for evaluating integrals that cannot be solved analytically and is commonly used in various fields such as physics, engineering, and finance.

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